Net adsorption: a thermodynamic framework for supercritical gas adsorption and storage in porous solids

The thermodynamic treatment of adsorption phenomena is based on the Gibbs dividing surface, which is conceptually clear for a flat surface. On a flat surface, the primary extensive property is the area of the solid. As applications became more significant, necessitating microporous solids, early researchers such as McBain and Coolidge implemented the Gibbs definition by invoking a reference state for microporous solids. The mass of solid is used as a primary extensive property because surface area loses its physical meaning for microporous solids. A reference state is used to fix the hypothetical hyperdividing surface typically using helium as a probe molecule, resulting in the commonly used excess adsorption; experimentalists measure this reference state for each new sample. Molecular simulations, however, provide absolute adsorption. Theoreticians perform helium simulations to convert absolute to excess adsorption, mimicking experiments for comparison. This current structure of adsorption thermodynamics is rigorous (if the conditions for reference state helium measurements are completely disclosed) but laborious. In addition, many studies show that helium, or any other probe molecule for that matter, does adsorb, albeit to a small extent. We propose a novel thermodynamic framework, net adsorption, which completely circumvents the use of probe molecules to fix the reference state for each microporous sample. Using net adsorption, experimentalists calibrate their apparatus only once without any sample in the system. Theoreticians can directly calculate net adsorption; no additional simulations with a probe gas are necessary. Net adsorption also provides a direct indication of the density enhancement achieved (by using an adsorbent) over simple compression for gas (e.g., hydrogen) storage applications.     

Appropriate volumes for adsorption isotherm studies: the absolute void volume, accessible pore volume and enclosing particle volume

In adsorption studies the choice of an appropriate void volume in the calculation of the adsorption isotherm is very crucial. It is often taken to be the apparent volume as determined by the helium expansion experiments. Unfortunately this method has difficulties especially when dealing with microporous solids, in which adsorption of helium might become significant at ambient temperatures. The amount adsorbed is traditionally obtained as the excess amount and the term "excess" refers to the excess over the amount occupying the apparent volume that has the same density as the bulk gas density. This could give rise to the maximum in the plot of excess amount versus pressure under supercritical conditions, and in some cases giving negative excess. Such behavior is difficult to analyze because the excess amount is not amenable to any classical thermodynamic treatments. In this paper we will present a method to determine the absolute void volume, and in that sense this volume is independent of temperature and adsorbate. The volume that is accessible to the centers of gas molecules is also investigated, and it is called the accessible volume. This volume depends on the choice of adsorbate, and it is appropriate to use this volume to calculate the pore density because we can assess how dense the adsorbed phase is. In the quest to determine the "absolute" adsorption isotherm so that a thermodynamics analysis can be applied, it is necessary to introduce the concept of "enclosing" volume, which is essentially the volume that encloses all solid particles, including all void spaces in them. The amount adsorbed is defined by the number of molecules residing in this volume. Having these volumes, we can derive the geometrical accessible void volume inside the particle and the solid volume, from which the particle and solid densities can be calculated.     

Comparison of molecular simulation of adsorption with experiment

Experimental measurements of adsorption yield the surface excess. The Gibbs surface excess is the actual or absolute amount of gas contained in the pores less the amount of gas that would be present in the pores in the absence of gas-solid intermolecular forces. Molecular simulation of adsorption yields the absolute amount adsorbed. Comparison of simulated adsorption isotherms and heats of adsorption with experiment requires a conversion from absolute to excess variables. Molecular simulations of adsorption of methane in slit pores at room temperature show large differences between absolute and excess adsorption. The difference between absolute and excess adsorption may be ignored when the pore volume of the adsorbent is negligible compared to the adsorption second virial coefficient (V?B _1s ).     

Direct measurements of pore fluid density by vibrating tube densimetry

The densities of pore-confined fluids were measured for the first time by means of vibrating tube densimetry (VTD). A custom-built high-pressure, high-temperature vibrating tube densimeter was used to measure the densities of propane at subcritical and supercritical temperatures (between 35 and 97 °C) and carbon dioxide at supercritical temperatures (between 32 and 50 °C) saturating hydrophobic silica aerogel (0.2 g/cm(3), 90% porosity) synthesized inside Hastelloy U-tubes. Additionally, supercritical isotherms of excess adsorption for CO(2) and the same porous solid were measured gravimetrically using a precise magnetically coupled microbalance. Pore fluid densities and total adsorption isotherms increased monotonically with increasing density of the bulk fluid, in contrast to excess adsorption isotherms, which reached a maximum and then decreased toward zero or negative values above the critical density of the bulk fluid. The isotherms of confined fluid density and excess adsorption obtained by VTD contain additional information. For instance, the maxima of excess adsorption occur below the critical density of the bulk fluid at the beginning of the plateau region in the total adsorption, marking the end of the transition of pore fluid to a denser, liquidlike pore phase. Compression of the confined fluid significantly beyond the density of the bulk fluid at the same temperature was observed even at subcritical temperatures. The effect of pore confinement on the liquid-vapor critical temperature of propane was less than ~1.7 K. The results for propane and carbon dioxide showed similarity in the sense of the principle of corresponding states. Good quantitative agreement was obtained between excess adsorption isotherms determined from VTD total adsorption results and those measured gravimetrically at the same temperature, confirming the validity of the vibrating tube measurements. Thus, it is demonstrated that vibrating tube densimetry is a novel experimental approach capable of providing directly the average density of pore-confined fluids, and hence complementary to the conventional gravimetric or volumetric/piezometric adsorption techniques, which yield the excess adsorption (the Gibbsian surface excess).     

Comparison of molecular simulation of adsorption with experiment

Experimental measurements of adsorption yield the surface excess. The Gibbs surface excess is the actual or absolute amount of gas contained in the pores less the amount of gas that would be present in the pores in the absence of gas-solid intermolecular forces. Molecular simulation of adsorption yields the absolute amount adsorbed. Comparison of simulated adsorption isotherms and heats of adsorption with experiment requires a conversion from absolute to excess variables. Molecular simulations of adsorption of methane in slit pores at room temperature show large differences between absolute and excess adsorption. The difference between absolute and excess adsorption may be ignored when the pore volume of the adsorbent is negligible compared to the adsorption second virial coefficient (VB _1s ).     

Modeling of gas adsorption equilibrium over a wide range of pressure: a thermodynamic approach based on equation of state

A thermodynamic approach based on the Bender equation of state is suggested for the analysis of supercritical gas adsorption on activated carbons at high pressure. The approach accounts for the equality of the chemical potential in the adsorbed phase and that in the corresponding bulk phase and the distribution of elements of the adsorption volume (EAV) over the potential energy for gas-solid interaction. This scheme is extended to subcritical fluid adsorption and takes into account the phase transition in EAV. The method is adapted to gravimetric measurements of mass excess adsorption and has been applied to the adsorption of argon, nitrogen, methane, ethane, carbon dioxide, and helium on activated carbon Norit R1 in the temperature range from 25 to 70 degrees C. The distribution function of adsorption volume elements over potentials exhibits overlapping peaks and is consistently reproduced for different gases. It was found that the distribution function changes weakly with temperature, which was confirmed by its comparison with the distribution function obtained by the same method using nitrogen adsorption isotherm at 77 K. It was shown that parameters such as pore volume and skeleton density can be determined directly from adsorption measurements, while the conventional approach of helium expansion at room temperature can lead to erroneous results due to the adsorption of helium in small pores of activated carbon. The approach is a convenient tool for analysis and correlation of excess adsorption isotherms over a wide range of pressure and temperature. This approach can be readily extended to the analysis of multicomponent adsorption systems.     

A density functional theory for Lennard-Jones fluids in cylindrical pores and its applications to adsorption of nitrogen on MCM-41 materials

A density functional theory (DFT) constructed from the modified fundamental-measure theory and the modified Benedict-Webb-Rubin equation of state is presented. The Helmholtz free energy functional due to attractive interaction is expressed as a functional of attractive weighted-density in which the weight function is a mean-field-like type. An obvious advantage of the present theory is that it reproduces accurate bulk properties such as chemical potential, bulk pressure, vapor-liquid interfacial tension, and so forth when compared with molecular simulations and experiments with the same set of molecular parameters. Capabilities of the present DFT are demonstrated by its applicability to adsorption of argon and nitrogen on, respectively, a model cylindrical pore and mesoporous MCM-41 materials. Comparison of the theoretical results of argon in the model cylindrical pore with those from the newly published molecular simulations indicates that the present DFT predicts accurate average densities in the pore, slightly overestimates the pore pressure, and correctly describes the effect of the fluid-pore wall interaction on average densities and pressures in the pore. Application to adsorption of nitrogen on MCM-41 at 77.4 K shows that the present DFT predicts density profiles and adsorption isotherms in good agreement with those from molecular simulations and experiments. In contrast, the hysteresis loop of adsorption calculated from the mean-field theory shifts toward the low pressure region because a low bulk saturated pressure is produced from the mean-field equation of state. The present DFT offers a good way to describe the adsorption isotherms of porous materials as a function of temperature and pressure.     

Determination of absolute gas adsorption isotherms: simple method based on the potential theory for buoyancy effect correction of pure gas and gas mixtures adsorption

The absolute adsorption isotherms are necessary to correctly evaluate the selectivity of the adsorbent material or to design adsorption processes at high pressure (e.g., H₂ purification from syngas processes, removal of acid gas from natural gas,…). The aim of this work is thus to propose an easy method to correct the buoyancy effect of the bulk phase on the adsorbed phase volume during both pure gas and gas mixtures adsorption for pressures up to 10 MPa. The potential theory of adsorption and the Dubinin–Radushkevich relation are adapted by introducing mixing parameters based on simple Berthelot rules. The concept of internal pressure used to characterize the adsorbed phase is also adapted for mixtures. The method is then improved on a commercial activated carbon (AC), when adsorbing pure H₂S and CH₄, and their mixtures up to 5 MPa. The study points out the importance to carefully consider the buoyancy effect of the bulk phase on the adsorbed phase volume. Its impact on the adsorbent material selectivity at high pressures could affect the design and the performances of PSA or TSA processes. For example, only considering the excess adsorption data leads to an apparent selectivity 13 % greater than the absolute one for a concentration of 6 ppm of H₂S in a CH₄ matrix at 5 MPa (298 K) on the AC.     

Stockmayer流体在活性炭孔中的吸附的分子模拟

应用巨正则系综monteCarlo方法模拟Stockmayer流体[以一氯二氟甲烷(R22)为代表]在活性炭孔中的吸附。模拟中R22分子采用等效Stockmayer势能模型,狭缝碳孔墙采用10-4-3模型。通过模拟得到了最佳孔径,并在最佳孔径下,针对不同的主体压力及活性基团密度,得到了吸附等温线、孔中流体的局部密度分布图和较为直观的孔内流体分子的瞬时构象,分析了吸附等温线的特征及孔内流体的吸附结构,认为在0.0,1.0sites/nm^2的活性基团密度下的碳孔内分别发生物理及化学吸附,并确定了最佳操作压力,为工业设计合适的催化剂提供依据。     

Adsorption volume and absolute adsorption: 1. Adsorption from a gaseous phase

Important concepts of adsorption science, such as excess and absolute adsorption isotherms and adsorption space volume, are critically analyzed and their status is discussed. An adequate method is proposed for evaluating the adsorption volume of solid adsorbents having arbitrary structures from excess adsorption isotherms. The method is tested by the example of five adsorption systems examined at a wide range of equilibrium pressures.     

Validity of the Kelvin equation in estimation of small pore size by nitrogen adsorption

 We have investigated a practical lower limit of a pore-size estimation by the nitrogen desorption isotherms at 77 K using the Kelvin equation. Changes in pore size of porous silica glasses before and after the monolayer preadsorption of n-propylalcohol were estimated by measuring the nitrogen adsorption and desorption isotherms. These changes should correspond to the thickness of monolayer of adsorbed n-propylalcohol. The thickness of monolayers obtained for the samples whose pore sizes are below ca. 2 nm were underestimated, when the Kelvin equation was applied to the nitrogen desorption isotherms using the values of surface tension and molar volume of bulk liquid nitrogen at 77 K. Below ca. 2 nm pore radius a careful application of the Kelvin equation is required to estimate a pore size. These results suggest that a change in the physical properties of liquid nitrogen in such a small pore occurs. It is supposed that the interaction between the solid surface and adsorbate molecules causes the changes in the surface tension and density of liquid nitrogen in such a narrow pore. Received: 21 March 1997 Accepted: 18 July 1997     

Characterization of the hydrophobicity of mesoporous silicas and clays with silica pillars by water adsorption and DRIFT

The hydrophobic-hydrophilic properties of a solid are related to the material chemistry and, often, these properties are relevant to the applications of a particular material. Contrarily to what happens with other properties, such as specific surface areas or pore volumes, the methodologies to ascertain on the hydrophilicity of a porous material are not well defined. In this work, we discuss and relate the information on the hydrophobicity degree obtained from water adsorption isotherms and from diffuse reflectance infrared Fourier transform (DRIFT), in a set of porous materials. The studied materials were mainly mesoporous solids, namely of MCM-41 and SBA-15 types, two xerogels and also different porous clays heterostructures. Both techniques were informative on the hydrophobic-hydrophilic properties of the studied samples, but the correlation between the information obtained by each technique was not straightforward. Water adsorption isotherms are much more sensitive to the differences of the studied materials than the DRIFT spectra. For silica-based mesoporous materials with similar surface chemistry, the water adsorption process and hence, the hydrophobic-hydrophilic properties, is mainly dependent on the pore diameters. However, water adsorption is much more sensitive to changes in the nature of the adsorbent surface than to changes in the pore diameter.     

氮气和氧气在膜表面和狭缝孔内平衡吸附的分子模拟

采用巨正则系综的MonteCarlo方法(GCMC)模拟常温(T=303K)下,氮气和氧气在具有狭缝状膜孔的碳膜内的吸附.气体分子之间、气体分子与膜原子之间的相互作用均采用Shifted-Lennard-Jones势能模型.研究了303K和10MPa下,不同膜厚度和膜孔宽度时氧气在膜面和膜孔内的密度分布以及303K和压力从1MPa到10MPa变化时,氮气和氧气在狭缝膜孔内超额吸附等温线.实验结果表明,膜孔端口效应显著,膜厚和膜孔宽度对孔内吸附影响较大,而膜构型对膜面吸附影响显著.     

Surface excess free energy of simple fluids confined in cylindrical pores by isothermal-isobaric Monte Carlo: influence of pore size

Confined fluid properties are mainly determined by interfacial phenomena characterized by surface quantities. Based on a simple model of Lennard-Jones particles confined in a cylindrical pore, this study introduces a grand potential surface quantity to quantify the difference in the thermodynamic pressure between the bulk and the confined fluids. The usual surface tension gamma defined as this grand potential difference for the same chemical potential in both confined and bulk states is generally strongly dependent on both the chemical potential and temperature. It is proposed here to introduce another surface quantity zeta which measures the thermodynamic pressure difference between confined and bulk states for identical densities. It is shown that this quantity is much less dependent on confined fluid density or chemical potential. It is actually constant along the gas-like and liquid-like adsorption/desorption branches for an irreversible isotherm (hysteresis), with a different value for each branch. For reversible supercritical isotherms, zeta is shown to remain constant in the low and high density parts of the isotherm. This independence on chemical potential (or equivalently fluid density) is believed to be of great interest for practical applications when one desires to calculate thermodynamic quantities such as the usual surface tension gamma or the thermodynamic pressure of a confined fluid for any given chemical potential and temperature. Such calculations are required to determine fundamental properties such as metastability or coexistence. The effects of temperature, fluid/substrate interaction strength, and pore size are studied.     

Effect of temperature on the adsorption of water in porous carbons

We report experimental and simulation studies to investigate the effect of temperature on the adsorption isotherms for water in carbons. Adsorption isotherms are measured by a gravimetric technique in carbon-fiber monoliths at 378 and 423 K and studied by molecular simulation in ideal carbon pores in the temperature range 298-600 K. Experimental adsorption isotherms show a gradual water uptake, as the pressure increases, and narrow adsorption-desorption hysteresis loops. In contrast, simulated adsorption isotherms at room temperature are characterized by negligible uptake at low pressures, sudden and complete pore filling once a threshold pressure is reached, and wide adsorption-desorption hysteresis loops. As the temperature increases, the relative pressure at which pore filling occurs increases and the size of the hysteresis loop decreases. Experimental adsorption-desorption hysteresis loops are narrower than those from simulation. Discrepancies between simulation and experimental results are attributed to heterogeneities in chemical composition, pore connectivity, and nonuniform pore-size distribution, which are not accounted for in the simulation model. The hysteresis phase diagram for confined water is obtained by recording the pressure-density conditions that bound the simulated hysteresis loop at each temperature. We find that the hysteresis critical temperature, i.e., the lowest temperature at which no hysteresis is detected, can be hundreds of degrees lower than the vapor-liquid critical temperature for bulk model water. The properties of confined water are discussed with the aid of simulation snapshots and by analyzing the structure of the confined fluid.     

Grand canonical monte carlo simulation study of methane adsorption at an open graphite surface and in slit-like carbon pores at 273 K

Grand canonical Monte Carlo (GCMC) simulation was used for the systematic investigation of the supercritical methane adsorption at 273 K on an open graphite surface and in slit-like micropores of different sizes. For both considered adsorption systems the calculated excess adsorption isotherms exhibit a maximum. The effect of the pore size on the maximum surface excess and isosteric enthalpy of adsorption for methane storage at 273 K is discussed. The microscopic detailed picture of methane densification near the homogeneous graphite wall and in slit-like pores at 273 K is presented with selected local density profiles and snapshots. Finally, the reliable pore size distributions, obtained in the range of the microporosity, for two pitch-based microporous activated carbon fibers are calculated from the local excess adsorption isotherms obtained via the GCMC simulation. The current systematic study of supercritical methane adsorption both on an open graphite surface and in slit-like micropores performed by the GCMC summarizes recent investigations performed at slightly different temperatures and usually a lower pressure range by advanced methods based on the statistical thermodynamics.     

Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. II. Adsorption of atomic and molecular fluids in a porous material

We propose to apply expanded Wang-Landau simulations to study the adsorption of atomic and molecular fluids in porous materials. This approach relies on a uniform sampling of the number of atoms and molecules adsorbed. The method consists in determining a high-accuracy estimate of the grand-canonical partition function for the adsorbed fluids. Then, using the formalism of statistical mechanics, we calculate absolute and excess thermodynamic properties relevant to adsorption processes. In this paper, we examine the adsorption of argon and carbon dioxide in the isoreticular metal-organic framework (IRMOF-1). We assess the reliability of the method by showing that the predicted adsorption isotherms and isosteric heats are in excellent agreement with simulation results obtained from grand-canonical Monte Carlo simulations. We also show that the proposed method is very efficient since a single expanded Wang-Landau simulation run at a given temperature provides the whole adsorption isotherm. Moreover, this approach provides a direct access to a wide range of thermodynamic properties, such as, e.g., the excess Gibbs free energy and the excess entropy of adsorption.     

Net,excess and absolute adsorption and adsorption of helium

The definitions of absolute, excess and net adsorption in microporous materials are used to identify the correct limits at zero and infinite pressure. Absolute adsorption is shown to be the fundamental thermodynamic property and methods to determine the solid density that includes the micropore volume are discussed. A simple means to define when it is necessary to distinguish between the three definitions at low pressure is presented. To highlight the practical implications of the analysis the case of adsorption of helium is considered in detail and a combination of experiments and molecular simulations is used to clarify how to interpret adsorption measurements for weakly adsorbed components.     

Calculation of immersion enthalpy data from adsorption isotherms

The thermodynamic equations for the calculation of binary and ternary immersion data in excess formalism are presented. Immersion enthalpies and entropies of the n-hexane/n-octane, n-octane/n-tetradecane and n-hexane/n-tetradecane binary mixtures as well as the n-hexane/n-octane/n-tetradecane ternary mixture on activated carbon are calculated from the temperature dependence of adsorption isotherms. In order to evaluate the quality of the calculations, the calculated immersion enthalpies of the binary mixtures on activated carbon are compared with those that were measured calorimetrically. It is shown that phenomenological thermodynamics can be used successfully to predict calorimetric data on the basis of adsorption excess isotherms.